11). The equation \( \Large \left(a+b\right)^{2}=4ab \sin^{2} \theta \) is possible only when
| A). \( \Large a = b \) |
| B). \( \Large 2a = b \) |
| C). \( \Large a = 2b \) |
| D). none of these |
|
12). The value of the expression \( \Large 1 - \frac{\sin^{2} y}{1+\cos y}+\frac{1 + \cos y}{\sin y}-\frac{\sin y}{1- \cos y} \) is equal to;
| A). 0 |
| B). 1 |
| C). \( \Large \sin y \) |
| D). \( \Large \cos y \) |
|
13). The circular wire of diameter 10 cm is cut and placed along the circumference of a circle of diameter 1m. The angle subtended by the write at the centre of the circle is equal to:
| A). \( \Large \frac{ \pi }{4}rad \) |
| B). \( \Large \frac{ \pi }{3}rad \) |
| C). \( \Large \frac{ \pi }{5}rad \) |
| D). \( \Large \frac{ \pi }{10}rad \) |
|
14). The greatest and least value of \( \Large \sin x \cos\ x \) are:
| A). 1, -1 |
| B). \( \Large \frac{1}{2},\ -\frac{1}{2} \) |
| C). \( \Large \frac{1}{4},\ -\frac{1}{4} \) |
| D). 2, -2 |
|
15). If \( \Large A = \sin^{2} \theta + \cos^{4} \theta \), then for all real values of \( \Large \theta \)
| A). \( \Large 1 \le A \le 2 \) |
| B). \( \Large \frac{3}{4} \le A \le 1 \) |
| C). \( \Large \frac{13}{16} \le A \le 1 \) |
| D). \( \Large \frac{3}{4} \le A \le \frac{13}{16} \) |
|
16). \( \Large \tan \frac{2 \pi }{5} - \tan \frac{ \pi }{15} - \sqrt{3} \tan \frac{2 \pi }{5} \tan \frac{ \pi }{15} \) is equal to:
| A). \( \Large -\sqrt{3} \) |
| B). \( \Large \frac{1}{\sqrt{3}} \) |
| C). \( \Large 1 \) |
| D). \( \Large \sqrt{3} \) |
|
17). If \( \Large A = 130 ^{\circ} and\ x=\sin A + \cos A \), then:
| A). \( \Large x > 0 \) |
| B). \( \Large x < 0 \) |
| C). \( \Large x=0 \) |
| D). \( \Large x \le 0 \) |
|
18). If \( \Large A+B+C= \pi \ and\ \cos A = B \cos C,\ then\ \tan B \tan C \) is equal to:
| A). \( \Large \frac{1}{2} \) |
| B). 2 |
| C). 1 |
| D). \( \Large -\frac{1}{2} \) |
|
19). The period of \( \Large \sin^{2} \theta \) is
| A). \( \Large \pi ^{2} \) |
| B). \( \Large \pi \) |
| C). \( \Large 2 \pi \) |
| D). \( \Large \frac{ \pi }{2} \) |
|
20). If \( \Large y = \sin^{2} \theta + cosec^{2} \theta \), \( \Large \theta \ne 0 \), then
| A). \( \Large y = 0 \) |
| B). \( \Large y \le 2 \) |
| C). \( \Large y \ge -2 \) |
| D). \( \Large y > 2 \) |
|
